Beat the eggs with the sugar very well. In some recipe versions of this cake, they beat the yolks with the sugar first and add the whipped egg whites at the end.
While stirring nonstop, pour in the butter and water. Then add the sifted flour with the baking powder and vanilla, while stirring with a wooden spoon. Pour the mixture into a rectangular oven dish laid out with baking paper and bake about 35-40 min. in a preheated 356°F (180 °C) oven.
Mix the cream, milk and sugar in a large bowl and stir for about 10 min.
Start making the caramel after you put the cake in the oven. Put the sugar with the butter in a container on the stove on low heat so it starts to caramelize but don't stir. Once the caramel forms, add the milk and cream (in several lots) and stir vigorously. Even if the sugar hardens, don't worry - it will dissolve once again when stirred.
Stick a skewer in the cake while it's still hot and pour on the cream topping. Wait for it to soak in and distribute the caramel on top.